General Information
| Student: | Andrew Xie |
|---|---|
| Office: | CoRE 444 |
| School: | Rutgers University |
| E-mail: | andrew.x@rutgers.edu |
| Project: | Persistent Homology in the study of structure and memory in dynamic networks |
Project Description
TODO
Weekly Log
- Week 0:
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Much of this week was spent learning background material and defining possible research directions.
In particular, we read about poset-indexed persistence modules (most importantly zigzag persistence), which allows for non-monotone filtrations used to analyze dynamic data. We also reviewed Tom Needham's book on applied algebraic topology for general persistence theory, and have prepared a short talk of selected topics.
We explored applications of TDA to neuroscience, such as the paper by Chowdhury, Dai and Memoli which shows that "forgetting" (enabled by zigzag persistence) improves topological recovery of features.
In addition, Prof. Memoli has given us a few talks on Gromov-Hausdorff distance and dynamic metric spaces, and posed a few interesting questions about G-H distance between spheres and intervals/trees
Additional Information
Acknowledgements
This research is supported by NSF grant IIS-2524678 and the Rutgers Math Department